It is interesting to note that the large area to the left and the small area to the right in the ENT image does conform somewhat to where extra image area would be if the 35mm film from "Ménage à Troi" wasn't hard matted in-camera.

Perhaps director Rob Legato (one of TNG's VFX Supervisors) decided that for his episode he wasn't going to hard-matte the image in-camera.

But if that is the case -- why did they also have to crop the top and bottom of the image for ENT?

Another possibility was that this practice of hard-matting in-camera was inconsistent during TNG's run and simply resulted in a stroke of good luck for this particular shot being used in ENT?

Because even with the extra material on the side 35mm still is not 16x9 widescreen. The only way to have TNG in 16x9 is to crop the top and bottom. Using the extra material on the side just means you don't have to crop off as much. Although that extra material might not always be useable. There could be mikes, exposed frames, or any number of other problems with the extra information which was ignored since they weren't using it for the 4x3 TV screen.

Of course, realistically if TNG ever gets remastered it will be 4x3 just like TOS-R is 4x3. The real challenge with TNG is having to redo every edit and FX shot since it was all done on video and not film.